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Mirrors > Home > ILE Home > Th. List > imaeq2 | Unicode version |
Description: Equality theorem for image. (Contributed by NM, 14-Aug-1994.) |
Ref | Expression |
---|---|
imaeq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reseq2 4862 | . . 3 | |
2 | 1 | rneqd 4816 | . 2 |
3 | df-ima 4600 | . 2 | |
4 | df-ima 4600 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 crn 4588 cres 4589 cima 4590 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 df-opab 4027 df-xp 4593 df-cnv 4595 df-dm 4597 df-rn 4598 df-res 4599 df-ima 4600 |
This theorem is referenced by: imaeq2i 4927 imaeq2d 4929 ssimaex 5530 ssimaexg 5531 isoselem 5771 f1opw2 6027 fopwdom 6782 ssenen 6797 fiintim 6874 fidcenumlemrk 6899 fidcenumlemr 6900 sbthlem2 6903 isbth 6912 ennnfonelemp1 12177 ennnfonelemnn0 12193 ctinfomlemom 12198 ctinfom 12199 tgcn 12650 iscnp4 12660 cnpnei 12661 cnima 12662 cnconst2 12675 cnrest2 12678 cnptoprest 12681 txcnp 12713 txcnmpt 12715 metcnp3 12953 |
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